Abstract This work is focused on the numerical modeling of steady laminar natural convection flow in an annulus filled with water–alumina nanofluid. The inner surface of the annulus is heated uniformly by a uniform heat flux q and the outer boundary is kept at a constant temperature T c . Two thermal conductivity models namely, the Chon et al. model and the Maxwell Garnett model, are used to evaluate the heat transfer enhancement in the annulus. The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite-element method. A parametric study is conducted and a selective set of graphical results is presented and discussed to illustrate the effects of the presence of nanoparticles, the Prandtl number and the Grashof number on the flow and heat transfer characteristics for both nanofluid models. It is found that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by increasing the nanoparticles volume fraction and Prandtl number at moderate and large Grashof number using both models. However, for the Chon et al. model the greatest heat transfer rate is obtained.